Well temperament: Difference between revisions
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As a consequence of their irregularity, it is possible in extreme cases for well temperaments to have classes where they tune each instance of an interval in that class uniquely, as if they were [[Just intonation|just]] scales of the same [[rank]] as their cardinality. For example, one may make a well temperament from a [[EdIX|nonet]] by taking m [[EDF|edf]] alternating with m equal divisions of an (n [[edo]]) interval between 600 and 800 [[Cent (music)|cent]]<nowiki/>s though an interval very close to 600 or 800 cents is going to make a well temperament sounding little like a nonet. Each tone of such a well temperament will have a unique fifth either above or below it. | As a consequence of their irregularity, it is possible in extreme cases for well temperaments to have classes where they tune each instance of an interval in that class uniquely, as if they were [[Just intonation|just]] scales of the same [[rank]] as their cardinality. For example, one may make a well temperament from a [[EdIX|nonet]] by taking m [[EDF|edf]] alternating with m equal divisions of an (n [[edo]]) interval between 600 and 800 [[Cent (music)|cent]]<nowiki/>s though an interval very close to 600 or 800 cents is going to make a well temperament sounding little like a nonet. Each tone of m edf in such a well temperament will have a unique fifth either above or below it. | ||
== Individual pages for WTNs == | == Individual pages for WTNs == | ||
Revision as of 03:24, 30 May 2021
A well temperament is a circulating temperament where the intervals in a class are not all tuned the same. It is intermediate between an equal temperament, where all of the intervals in the class are tuned the same, and a MOS scale, where for a class containing a generator all but one of the intervals are tuned the same.
- Kirnberger – Kirnberger temperament
- the fifths are pure, except for
- the C–G, D–A, G–D and A–E fifths are quarter comma meantone
- the F#–Db is the wolf fifth, a schisma flat
- Vallotti – Vallotti/Young temperament
- the fifths are pure, except for
- the C–G, D–A, E–B, F–C, G–D and A–E fifths are 1/6 Pythagorean comma flat.
As a consequence of their irregularity, it is possible in extreme cases for well temperaments to have classes where they tune each instance of an interval in that class uniquely, as if they were just scales of the same rank as their cardinality. For example, one may make a well temperament from a nonet by taking m edf alternating with m equal divisions of an (n edo) interval between 600 and 800 cents though an interval very close to 600 or 800 cents is going to make a well temperament sounding little like a nonet. Each tone of m edf in such a well temperament will have a unique fifth either above or below it.
Individual pages for WTNs
- 4wtn
- 6wtn
- 8wtn
- 10wtn
- 12wtn
- 14wtn
- 16wtn
- 18wtn
- 20wtn
- 22wtn
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- 106wtn
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- 110wtn
- 112wtn
- 114wtn
- 116wtn
- 118wtn